Traditional diagnostic methods require information from medical imaging technologies and chemical analysis of bodily fluids. Medical imaging technologies such as Magnetic Resonance Imaging (MRI), Computed Tomography (CT), Positron Emission Tomography (PET) or Ultrasound scans can provide highly detailed geometrical information about a patient's internal organs. They accomplish this by mapping out the geometrical distribution of internal tissues or fluid. It is widely used for diagnosing physical illness such as tumours or injuries. Chemical analysis of biological samples can provide detailed information about chemical composition within the body.
The drawback of medical imaging, however, is that it provides only geometric information but contains little information about composition. Chemical and/or biological analysis on the other hand provides composition but not geometry. Certain illnesses, such as traumatic brain injuries, are often difficult to detect with medical imaging as these injuries do not show any initial symptoms and can be hard to localize or deteriorate too fast for chemical analysis, thus making it difficult to treat many patients effectively. The present invention proposes the use of dispersive ultrasound as a non-invasive diagnostic system for traumatic brain injury.
In general, ultrasound refers to longitudinal mechanical waves with high frequencies in the range of MHz. Ultrasound systems have traditionally been used for medical or industrial imaging, wherein ultrasound reflection points are mapped out in order to build up an internal image of the target. These systems return information about the internal structure of a target but not its composition.
Dispersion is an effect in which the non-linear, frequency-dependent bulk modulus of the medium results in different propagation speeds for different sound frequencies. Since the properties of the bulk modulus depend on the specific characteristics of the medium, such as density, composition, mixture concentration, distribution and in some situations chemical composition, the pattern of frequency-dependent propagation speeds can be used to identify the medium. In other words, the dispersive effect is the result of different propagation speeds for different frequencies. As can be seen in Equations (1) and (2), the propagation speed c(f) as a function of frequency has a dependency on elasticity Kv for liquid media and the bulk modulus KB for solid media.
                                                                        c                ⁡                                  (                  f                  )                                            =                                                                                          K                      v                                        ⁡                                          (                      f                      )                                                                                                  ρ                      0                                        ·                                          β                      ad                                                                                                                              for              ⁢                                                          ⁢              liquid              ⁢                                                          ⁢              media                                                          (        1        )                                                                                    c                ⁡                                  (                  f                  )                                            =                                                                                          K                      B                                        ⁡                                          (                      f                      )                                                                            ρ                    0                                                                                                          for              ⁢                                                          ⁢              solid              ⁢                                                          ⁢              media                                                          (        2        )            
Thus, a Dispersive Ultrasound System (DUS) measures the ultrasound dispersion patterns of different media and uses these patterns for identification. A DUS utilizes ultrasound pulses of different frequencies to interrogate a medium in order to provide propagation times for each of the transmitted frequencies. This process provides estimates of the dispersion patterns c(f) for a specific contained medium. Since each medium has a unique bulk modulus, a DUS can identify unknown contained media by matching the dispersion pattern of the unknown sample with a previously established library of dispersion patterns of known media.
The observed changes to the propagation speed are usually very small and require a very precise measurement of the propagation speed. Instead of measuring the speed of sound in the media, it is easier to accurately measure the propagation time of ultrasound signals that travel along a known distance from a transmitter T to a receiver R, as depicted in FIG. 1.
As shown by Equation (3), the propagation speed c(f) can be estimated from the propagation time t(f) by assuming that the constant dimension d, is known.
                              c          ⁡                      (            f            )                          =                  d                      t            ⁡                          (              f              )                                                          (        3        )            
One way to very accurately measure the propagation time t(f) required for the signal to travel from the transmitter to the receiver is by using a very high sampling frequency for the received signal. To achieve the necessary accuracy, however, a sampling frequency in the GHz range would be necessary. Such a system would be formidably expensive and have unacceptable power requirements for a portable device. Instead, we observe that an ultrasound signal is not only described by its frequency but also by phase information:x(t)=A·sin(2πf·t+φ)  (4)
Therefore, to overcome the requirement for a high sampling frequency, the phase information of the ultrasound wave can be used along with its amplitude to provide accurate estimates of propagation times.
It is commonly known that the phase information only covers a range from −π to +π. Hence, it can only be used to get additional information about one period of the signal. Beyond that, this information keeps repeating itself. Using a phenomenon from wave theory called beat-note, which is the result of the combination of two acoustic continuous wave signals that are close in pitch but yet not identical. The difference in frequency generates the beating. The frequency of the beat-note is given by:fbeat=f1f2  (5)
The closer f1 and f2 are, the lower is the resulting frequency fbeat and the longer is the period of the resulting beat phase Tbeat=1/fbeat. The use of the beat-note approach allows for the unique identification of a certain point in the signal. Once this unique point has been found, the phase information of the individual frequency can be used to accurately calculate propagation times.
Phase information is not limited by the sample rate, and therefore can provide nanosecond scale precision using sample rates only in the megahertz range. The complication with this approach however is the need to resolve the phase ambiguity problem, arising from the fact that phase information wraps around for every change in propagation time greater than a single period in the signal, as was discussed in the previous section.
An early approach (Stergiopoulos et al., 2008, “Non-invasive monitoring of vital signs and traumatic brain injuries”, Defence R&D Canada—Toronto, Department of National Defence, (Technical Report), DRDC Toronto, TR 2008-105; U.S. Pat. No. 7,854,701) to solving the phase ambiguity problem used two closely spaced component frequencies to create a pair of high and low side image frequencies, that is, when the product of the two component frequencies are taken, they produce a new signal that is made up of two component signals, each with frequencies and phase at the sum and difference of the component frequencies:
                              sin          ⁢                                          ⁢                      (                                          2                ⁢                π                ⁢                                                                  ⁢                                  f                  1                                            +                              ϕ                1                                      )                    ⁢          sin          ⁢                                          ⁢                      (                                          2                ⁢                π                ⁢                                                                  ⁢                                  f                  2                                            +                              ϕ                2                                      )                          =                              (                                          cos                ⁡                                  (                                                            2                      ⁢                                              π                        ⁡                                                  (                                                                                    f                              1                                                        -                                                          f                              2                                                                                )                                                                                      +                                          (                                                                        ϕ                          1                                                -                                                  ϕ                          2                                                                    )                                                        )                                            -                              cos                ⁡                                  (                                                            2                      ⁢                                              π                        ⁡                                                  (                                                                                    f                              1                                                        +                                                          f                              2                                                                                )                                                                                      +                                          (                                                                        ϕ                          1                                                +                                                  ϕ                          2                                                                    )                                                        )                                                              2                                    (        6        )            
The two resulting frequencies are called the high side image frequency (f1+f2) and the low side image frequency (f1−f2); and they should satisfy Eq. (7), which requires also a variable sampling rate. With a small enough frequency difference between the component frequencies, each cycle of the low side image frequency could span the entire transmission and reception pulse of the component signals. It was assumed that the frequencies of the component signals would be close enough that dispersive effects between them would be negligible. The phase position of the low side image frequency could then be used to match each cycle in the transmitted signal to its counterpart in the received signal, therefore solving the phase ambiguity problem.
                                                                        f                t                                            f                s                                      ≠                          m              n                                ;                      with            ⁢                                                  ⁢            m                          ,                  n          ∈          N                                    (        7        )            
It was later determined that there is a reciprocal relationship between the frequency spacing of the component signals and the accuracy and sensitivity of the low side image signal's phase information.
As the frequency difference becomes smaller, the period of the low side image signal grows larger relative to the component signals' period, increasing the precision required in marking its phase. Furthermore, since the phase of the low side image signal is directly related to the phase difference of the component frequencies, any slight dispersion will cause the image signal to shift in phase by the same amount. Compounded with the increased precision requirement, the negligible dispersion assumption does not translate into negligible error, and phase ambiguity can not be resolved reliably with this method under all dispersion conditions.
In other words, the previous method described in Stergiopoulos et al., 2008 and U.S. Pat. No. 7,854,701 was based upon the beat-note and the assumption that the dispersive effect is negligible for the two component frequencies. However, simple simulations can show that this assumption is very limited. As an example, let us consider two signals with frequencies f1=4.33333 MHz and f2=4.6666666 MHz are used. According to Equation (5), the beat time for these two frequencies is 3 μs. Assuming there is no dispersion in the propagation speed of the ultrasound signals, then for this example c=1540 m/s. The resulting beat phase is shown in FIG. 2. Furthermore, it is assumed that the zero crossing of the beat phase is the point the system uses to calculate the time. Bushong and Archer (Bushong and Archer, 1991, “Diagnostic Ultrasound”, Mosby Inc,) define the speed of sound for an aqueous human haemoglobin solution as:
                              c                      (            f            )                          =                              (                          1523.83              +                              0.4013                ·                                  log                  ⁡                                      (                    f                    )                                                                        )                    ⁢                      m            s                                              (        8        )            
The difference in speed for the two above frequencies results is then:
                              Δ          ⁢                                          ⁢                      c                          (              f              )                                      =                                                            (                                  1523.83                  +                                      0.4013                    ·                                          log                      ⁡                                              (                                                  4.3                          ×                                                      10                            6                                                                          )                                                                                            )                            ⁢                              m                s                                      -                                          (                                  1523.83                  +                                      0.4013                    ·                                          log                      ⁡                                              (                                                  4.6                          ×                                                      10                            6                                                                          )                                                                                            )                            ⁢                              m                s                                              =                      12.3            ⁢                          m              s                                                          (        9        )            
If now the speed of sound only changes by 5 m/s for the frequency f2, the resulting beat information changes to the one shown in FIG. 2. As a result, the initially used calibration point has moved into a completely different period than it was before. The error of this method grows with the bandwidth used and prevents the acquisition of reliable data sets. This may have an impact in providing reliable diagnosis, as discussed herein.